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Re: NMinimize problem: fct minimized uses FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg123547] Re: NMinimize problem: fct minimized uses FindRoot
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Sun, 11 Dec 2011 03:45:02 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201112101227.HAA19219@smc.vnet.net>

To prevent NMinimize and FindMinimum from evaluating your function 
symbolically, you could define MyNumFct according to

Clear[MyNumFct];
MyNumFct[optvar_?NumericQ] :=
 Module[{inteq, n}, inteq[x_] := (Sin[x] + 1/2*Cos[x])/optvar;
  n = n /. FindRoot[inteq[n], {n, 0.1}];
  Return[n + Sin[optvar]];]



Heike.

On 10 Dec 2011, at 13:27, Doug Tinkham wrote:

> Hello
>
> I'm using NMinimize and FindMinimum to minimize a function that uses
> FindRoot when calculating it's value. The problem is that the equation
> that FindRoot is used on uses the variable that is being optimized, and
> Mathematica appears to be forcing the variable that is being optimized
> to remain symbolic in the FindRoot call, and this leads to recursion and
> a recursion limit error.
>
> Rather than post my actual functions that are quite long, I've reduced
> my problem to the code below that shows my issue. As you will see,
> FindRoot keeps optvar in symbolic form when executing FindRoot. Is there
> a way to force Mathematica to use all numerical calculations using
> NMinimize or FindMinimum?  Is the issue with calculation of the
> gradient, which Mathematica wants to do symbolically?
>
> Many thanks.
>
>
>
> MyNumFct[optvar_] := Module[{inteq, n},
>  inteq[x_] := (Sin[x] + 1/2*Cos[x])/optvar;
>  n = n /. FindRoot[inteq[n], {n, 0.1}];
>  Return[n + Sin[optvar]];
> ]
>
> NMinimize[{MyNumFct[var], 0 <= var <= 6}, {var, 4.1}]
>
>

• References:
  • NMinimize problem: fct minimized uses FindRoot
    • From: "Doug Tinkham" <dtinkham@live.ca>